Hi everyone,
i have to deliver a paper for my course, i solved the problem and made the close form, but my instructor told me to use gams for sensitivity analysis,
if you have a gams model like the below please share with me so i con use it to formulate my problem.
thanks in advance… Necip
CASE 7 BestChip: Expansion Strategy
BestChip (BC) is a large nationwide corporation that produces low-fat snack products for an expanding market (pun intended). Basically, BC takes materials (corn, wheat, and potatoes) and turns them into two types of snacks: chips (regular and green onion) and party mix (one variety). BC is expanding into the western United States and is considering sites for locating production facilities.
BC currently has eight candidate sites. Table 20 shows the sites ‘purchase prices and the purchase and shipping cost per ton of each material to each site.
The purchase cost represents the yearly amortized cost of opening and operating the site (exclusive of uses of the models.
Each site may produce as many as 20,000 tons of product per year.
BC has six major customers, and all demand is shipped by truck from the plant to the customer warehouse. The shipping cost depends on the tonnage and distance and comes to $0.15 per ton-mile. The customers, their location, and their yearly demand in tons for each product are listed in Table 21. You must meet demand.
The makeup of the products does not depend on the production plant. Table 2 gives the productingredient mix data. The company requires that we consolidate our business, so we cannot locate plants in more than two states.
For this analysis, ignore the differences in property and income tax rates between the states (this is usually critical, but it gets us far afield of the key issue of math programming). In addition, many critical factors actually determine locations; for example, the method of financing the site purchase will also be a major factor in the decision—but we will ignore that also.
Your job is to determine how we should expand into the west and develop alternatives. Questions you should answer include:
What sites should be selected? How should the customers be served?
If gasoline gets more expensive and our trucking costs change, then how is the recommendation affected?
If rail freight costs for material shipping increase, then how is the recommendation affected?
Please consider other sensitivity-analysis issues that you feel might be important for management’s decision-making process.
TABLE 20 Site Information and Material Shipping Cost
TABLE 21 Demand Information
TABLE 2 Product-Ingredient Mix
SOLUTION
Number the plants, customers, products, ingredients, and states:
i as Plant in
1 Yuma, AZ
2 Fresno, CA
3 Tueson, AZ
4 Pomona, CA
5 Santa Fe, NM
6 Flagstaff, AZ
7 Las Vegas, NY
8 St. George, UT
j as Customer & Location
1 Jones, Salt Lake City
2 YZCO, Albuquerque
3 Square Q, Phenix
4 AJ Stores, San Diego
5 Sun Quest, Los Angeles
6 Harm’s Path, Tucson
k as Product
1 Regular chips
2 Green onion chips
3 Party mix
l as ingredients
1 Corn
2 Wheat
3 Potato
s -
1
2
3
4
5
States
AZ
CA
NM
NV
UT
xijk  tons of product k sent from plant i to customer j;
yi  1, if plant i is open for production, 0 otherwise;
ïŽs  1, if states s is used, 0 otherwise.
We also define the following intermediate variables:
 fi  fixed cost associated with opening plant i.
i fi
1 125,000
2 130,000
3 140,000
4 160,000
5 150,000
6 170,000
7 155,000
8 115,000
cij  cost to ship 1 ton of final products from plant i to customer j.
Unit shipping cost from Plants i to Customers j ($0.15 times the mile distance)
dkj  demand in tons of product k from customer j.
mil  cost in dollars of sending 1 ton of raw material l to plant i.
rlk  percentage of product k that is raw material l.
We now have the following mixed ILP model
minz = Location purchasing cost+ Shipping for Products+ Shipping for Raw Materials
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CASE 7 BestChip.docx (60.1 KB)